Just returned from 4 days in Madrid and can recommend it highly - such a vibrant city, impressive architecture and art, great food at realistic prices, open air Sunday markets, fantastic night life and music, top class shopping including fab shoes and bags, plenty to see and do. The hop-on-off bus is a great way to get around all the main sights.
If you go, be sure to take a day trip to either (or both) Toledo and Segovia. Only problem (as in most big cities) appears to be pickpockets. Public transport is very easy to use and the weather in September should be very good - usually in the mid to late 20s at that time.